Topic
Average-case complexity
About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.
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Journal Article•
TL;DR: It is shown that a mild derandomization assumption together with the worst-case hardness of NP implies the average- case hardness of a language in non-deterministic quasi-polynomial time and that black-box techniques cannot prove such results.
Abstract: We show that a mild derandomization assumption together with the worst-case hardness of NP implies the average-case hardness of a language in non-deterministic quasi-polynomial time Previously such connections were only known for high classes such as EXP and PSPACE There has been a long line of research trying to explain our failure in proving worstcase to average-case reductions within NP [FF93, Vio03, BT03, AGGM06] The bottom line of this research is essentially that (under plausible assumptions) black-box techniques cannot prove such results Indeed, our proof is not black-box, as it uses a non-black-box reduction of Gutfreund, Shaltiel and Ta-Shma [GSTS05] Furthermore, we prove using the same arguments as the above mentioned negative results, that this reduction cannot be done in a black-box way (again, under a plausible assumption) Thus our techniques show a way to bypass black-box impossibility arguments regarding worst-case to average-case reductions
9 citations
11 Jul 1994
TL;DR: The average case complexity of a computational problem for arbitrary input distributions is defined using a complexity measure for the average delay of computational model circuits over the semigroup, called time.
Abstract: We analyse the average case complexity of evaluating all prefixes of an input vector over a given semigroup As computational model circuits over the semigroup are used and a complexity measure for the average delay of such circuits, called time, is introduced Based on this notion, we then define the average case complexity of a computational problem for arbitrary input distributions
9 citations
28 Aug 2006
TL;DR: The Lempel–Ziv complexity is investigated for one of the most important families of infinite words in combinatorics, namely the fixed points of morphisms, and a complete characterisation of the complexity classes is given, depending on the periodicity of the word and the growth function of the morphism.
Abstract: The Lempel–Ziv complexity is a fundamental measure of complexity for words, closely connected with the famous LZ77, LZ78 compression algorithms. We investigate this complexity measure for one of the most important families of infinite words in combinatorics, namely the fixed points of morphisms. We give a complete characterisation of the complexity classes which are Θ(1), Θ(logn), and Θ(n$^{\rm 1/{\it k}}$), k∈ℕ, k ≥2, depending on the periodicity of the word and the growth function of the morphism. The relation with the well-known classification of Ehrenfeucht, Lee, Rozenberg, and Pansiot for factor complexity classes is also investigated. The two measures complete each other, giving an improved picture for the complexity of these infinite words.
9 citations
11 Jul 1999
TL;DR: A general lower bound on the average-case complexity of Shellsort is proved: the average number of data-movements made by a p-pass Shellsort for any incremental sequence is Ω(pn 1+1/p ) for every p.
Abstract: We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a p-pass Shellsort for any incremental sequence is Ω(pn 1+1/p ) for every p. The proof method is an incompressibility argument based on Kolmogorov complexity. Using similar techniques, the average-case complexity of several other sorting algorithms is analyzed.
9 citations
Journal Article•
TL;DR: Using Rauzy graphs, Ferenczi proved that if a symbolic dynamical system has linear complexity then it is S-adic, and a new proof of this latter result using the notion of return words to a set of words is provided.
Abstract: Using Rauzy graphs, Ferenczi proved that if a symbolic dynamical system has linear complexity then it is S-adic. Being more specific, the result can also be proved for infinite words. We provide a new proof of this latter result using the notion of return words to a set of words.
9 citations